For a three-state quantum walk with a pairwise-coupling SU(3) coin (angles β, γ, with α fixed at π/4), spreading stays ballistic for all couplings while the speed and left-right asymmetry vary in structured ways across parameter space.
Stationary measures of three-state quantum walks on the one-dimensional lattice
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In this paper, we consider stationary measures of discrete-time three-state quantum walks including the Fourier and Grover walks in the one-dimensional lattice. We give non-uniform stationary measures by solving the corresponding eigenvalue problem. Our new method is based on a reduced matrix, which is different from the generating function approach in our previous work. As a corollary, the Fourier walk on the cycle has a stationary measure with a periodicity.
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Controlled dynamics of a multi-component discrete-time quantum walker
For a three-state quantum walk with a pairwise-coupling SU(3) coin (angles β, γ, with α fixed at π/4), spreading stays ballistic for all couplings while the speed and left-right asymmetry vary in structured ways across parameter space.